Spatial-temporal alignment of time series with different sampling rates based on cellular multi-objective whale optimization

Abstract

Aligning time series of different sampling rates is an important but challenging task. Current commonly used dynamic time warping methods usually suffer from pathological temporal singularity problem. In order to overcome this, we transform the alignment task to a spatial-temporal multi-objective optimization (MOO) problem. Existing MOO algorithms are always inefficient in finding Pareto optimal alignment solutions due to their insufficiency in maintaining convergence and diversity among the obtained Pareto solutions. In light of this, we propose a novel and efficient MOO algorithm Cell-MOWOA which integrates Cellular automata with the rising Whale Optimization Algorithm to find Pareto optimal alignment solutions. Innovative multi-variate non-linear cell state evolutionary rules are designed within Pareto solution external archive to improve the convergence and diversity of the Pareto solutions, and novel whale population updating mechanism is designed to accelerate the convergence to the Pareto front. Besides, new integer whale updating mechanism is presented to transform real-number whale solutions to integer whale solutions. Experimental results on 85 gold-standard UCR time series datasets showed that Cell-MOWOA outperformed six state-of-the-art baselines by 24.53% in average in increasing alignment accuracy and 42.66% in average in reducing singularity. Besides, it achieved outstanding runtime efficiency, especially on long time series datasets.